Massively parallel sequencing techniques are used for detection of fetal aneuploidy from samples that comprise fetal and maternal nucleic acids. Fetal DNA often constitutes less than 10% of the total DNA in a sample, for example, a maternal cell-free plasma sample. Sequencing a large number of polynucleotides to generate sufficient data for fetal aneuploidy detection can be expensive. Methods for randomly enriching fetal nucleic acids in cell-free maternal sample have been described, including enriching nucleic acids based on size, formaldehyde treatment, methylation status, or hybridization to oligonucleotide arrays. There is a need for a means of selectively enriching non-random fetal and maternal polynucleotide sequences in a way that facilitates aneuploidy detection by massively parallel sequencing techniques and increases the sensitivity of aneuploidy detection.